ECOS3022: Economics of Financial Markets
Lecture: 8
Date: 16/5/13
The primary content of this lecture was the pricing of options and some fundamental properties. For
a general call and put option, independent of whether American or European. Please note t

Term 1 2016
ECOS3022
Guillaume Roger
University of Sydney
Exercise set 5 interest rate and CAPM
These may take a while and some effort but you have all the necessary material in the class notes.
Question #1: impatience and interest rate
Consider a two-per

SCHOOL OF ECONOMICS
FACULTY OF ARTS AND SOCIAL SCIENCES
ECOS3022
The Economics of Financial Markets
Semester 1 , 2014
Unit Coordinator: Oleksii Birulin
Email: oleksii.birulin@sydney.edu.au
Office: Merewether 361
Tel: 90365047
Consultation times: TBA
Class

Insurance problem recast as optimal portfolio
Problem 1. Suppose w of initial wealth, an investor has access to asset that pays
v per unit but only in state 1. The asset costs p per unit. 1 and 1
1 are the
probabilities of the states. U = ln (W ) : How ma

Faculty of Arts and Social Sciences
School:
Economics
Department/Program:
Unit of Study:
ECOS3022 Economics of Financial Markets
Session:
S1 2015
U nit of Stu d y O u t line
Unit Coordinators
Unit coordinators are listed on undergraduate and postgraduate

Econ 3022
Lecture 5: introduction to General
Equilibrium.
Some background material
February 18, 2016
Econ 3022
General equilibrium
Why?
Econ 3022
General equilibrium
Trade involves exchange.
Who buys? Who sells?
How are prices determined?
How is a consume

ECOS 3022
Contingent claim economy
February 18, 2016
ECOS 3022
Contingent claim economy
Why?
We want to formalise the notion of General equilibrium and
pave the way to a Finance Economy.
ECOS 3022
Two-period contingent claim economy
A more general treatme

ECOS 3022
Properties of Equilibrium
Incomplete markets
February 18, 2016
ECOS 3022
Properties of equilibrium
A Financial Market Equilibrium displays important properties.
1
It is Pareto optimal
2
It features complete diversification of idiosyncratic risk

ECOS 3022
CAPM and portfolio holding
February 18, 2016
ECOS 3022
CAPM and portfolio holding
Content:
From C-CAPM to CAPM
Portfolio holding decisions
Assumed knowledge:
C-CAPM
Basic statistics
ECOS 3022
CAPM
The CAPM is commonly used in finance to price th

ECOS 3022
Risk and time
February 18, 2016
ECOS 3022
Risk and time
Content:
Valuation of risk and time
Impatience
Aggregate risk
Properties of equilibrium
Assumed knowledge: Content:
Some basic statistics
Compounding and discounting
ECOS 3022
Compounding a

ECOS3022
ECOS 3022 Lecture 2
February 18, 2016
ECOS3022
Optimization with equality constraints
Content:
the constraint set
Lagrange multipliers
Assumed knowledge:
partial differentiation and its background
vector calculus
some linear algebra
ECOS3022
Cons

Term 1 2015
ECOS3022
Guillaume Roger
University of Sydney
Application/Exercise #4: Finance economy.
Uncertainty and spot nancial markets
Consider an exchange economy with two periods (t = 0, 1), 1 good as in class
and S states in the second period so S +

ECOS 3022
Search in a Finance Economy
May 22, 2016
ECOS 3022
Search and Finance
Why?
We depart for centralised Walrasian markets and allow for
over-the-counter (OTC) trades.
Many assets are traded OTC; most derivatives are traded
OTC. It is an important f

5.1 An economy with von NeumannMorgenstern agents
5
Static finance economy
This is the key theory chapter of this book. We now combine the Arrow
DebreuRadner economy of chapters 2 and 3 with the von Neumann
Morgenstern utility of chapter 4. The payoff of

ECOS 3022
Production in a Finance Economy
May 11, 2016
ECOS 3022
Production in a Finance Economy
Why?
We extend what we know of a Finance Economy to allow for
production.
This specifically enable us to consider equity contracts in the
set of securities.
I

2
1
Introduction
1 Introduction
(1987), for instance, has examined the social costs of business cycles. This
is obviously important for economic policy making, but it is also important
for macroeconomic theory. To learn the answer to this question, we nee

ECOS3022
ECOS 3022 Lecture 2
February 18, 2016
ECOS3022
Optimization with equality constraints
Content:
the constraint set
Lagrange multipliers
Assumed knowledge:
partial dierentiation and its background
vector calculus
some linear algebra
ECOS3022
Constr

Term 1 2015
Ecos3022
Guillaume Roger
University of Sydney
Practice exercises; set #3
These are tutorial, or practice questions, for you to familiarise yourself
with the concepts that we use. Think of them as drills, or scales on the
piano: they are useful

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Term 1 2015
ECOS3022
Guillaume Roger
University of Sydney
Exercise set 6 dynamics
Consider a T -period economy with a single good and two types of agents
(i = a, b). They have the same utility function
u = ln x0 +
T
t E[ln xt ], t = 1, 2, ., T
t=1
where

38
3
Asset economy
3 Asset economy
More generally, a financial asset is defined by the event-contingent cash flow
it delivers.
For simplicity, consider a two-period model with S states, as shown in
Figure 2.2. A financial asset, call it j , is a vector,

Term 1 2016
ECOS3022
Guillaume Roger
University of Sydney
Exercise #4: Finance economy.
Uncertainty and spot financial markets
Consider an exchange economy with two periods (t = 0, 1), 1 good as in class
and S states in the second period so S + 1 in total

Static Finance Economy
()
Expected Utility Implications
1 / 49
Intertemporal NM utility
A risky decision is characterized by the agents NM utility function v ,
his initial wealth w , and the properties of the lottery he lives in
[x1 , 1 ; .; xS , S ].
The

Mean-Variance Analysis:
a special case of the expected utility theory.
()
MV approach
1 / 49
Case 1: quadratic utility
v (w ) = aw
bw 2 for w < a/2b.
The expected utility
S
E [v (w )] =
s v (ws ) = aE [w ]
bE w 2 =
s =1
b (E [w ])2
= aE [w ]
b2 [w ]
We u

Option Pricing
()
Options
1 / 31
Example
a bond and one risky asset, with
R=
1 4
1 0
the markets are complete.
We issue a call option with strike price 2 for risky asset. The payo of
the option ro = max frs 2, 0g = [2, 0]0 .
The option is equivalent to ho

Choice Under Uncertainty
()
Expected Utility
1 / 25
Lottery
Consider driving from A to B for an appointment.
If you get there in time with probability 1 = 95%, payo is x.
If there is a tra c jam (with probability 2 = 4.8%) you are late and
payo is 0.
If a

Exercise set 5
1. Exercise 4.2 from Lengwiler.
2. Consider the following lotteries on the outcomes cfw_5,1,0
p = (0:00; 1:00; 0:00); q = (0:10; 0:89; 0:01);
r = (0:10; 0:00; 0:90); s = (0:00; 0:11; 0:89):
(a) Show that there are lotteries on the outcomes